Enthalpy-based multiple-relaxation-time lattice Boltzmann method for solid-liquid phase-change heat transfer in metal foams

In this paper, an enthalpy-based multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed for solid-liquid phase-change heat transfer in metal foams under the local thermal nonequilibrium (LTNE) condition. The enthalpy-based MRT-LB method consists of three different MRT-LB models: one for flow field based on the generalized non-Darcy model, and the other two for phase-change material (PCM) and metal-foam temperature fields described by the LTNE model. The moving solid-liquid phase interface is implicitly tracked through the liquid fraction, which is simultaneously obtained when the energy equations of PCM and metal foam are solved. The present method has several distinctive features. First, as compared with previous studies, the present method avoids the iteration procedure; thus it retains the inherent merits of the standard LB method and is superior to the iteration method in terms of accuracy and computational efficiency. Second, a volumetric LB scheme instead of the bounce-back scheme is employed to realize the no-slip velocity condition in the interface and solid phase regions, which is consistent with the actual situation. Last but not least, the MRT collision model is employed, and with additional degrees of freedom, it has the ability to reduce the numerical diffusion across the phase interface induced by solid-liquid phase change. Numerical tests demonstrate that the present method can serve as an accurate and efficient numerical tool for studying metal-foam enhanced solid-liquid phase-change heat transfer in latent heat storage. Finally, comparisons and discussions are made to offer useful information for practical applications of the present method.